Sen. Feinstein said it would be "premature" to cut off aid. In addition, the top Republican on the Armed Services Committee, John McCain, R-Ariz., warned that the situation with Pakistan is "complicated."
The lead Republican on the Foreign Services Committee, Dick Lugar, R-Ind., said financial aid to Pakistan should be continued.
"We need this relationship," he said, adding that aid should be provided "with the proper oversight."
White House Press Secretary Jay Carney dubbed the partnership between the two countries "important," saying that while the United States does need to find out what information Pakistanis had about bin Laden, "the government has provided useful and important assistance and cooperation to us in the years of this struggle against terrorism."
House Speaker John Boehner on Wednesday also defended U.S. aid to Pakistan and warned that it was premature to discuss cutting off funding, saying the United States should have an "eyeball to eyeball conversation about where this relationship is going."
"I think we need more engagement, not less," Boehner said. "Having a robust partnership with Pakistan is critical to breaking the back of al Qaeda and the rest of them."
That still hasn't stopped his caucus members from voicing their opposition.
Rep. Ted Poe, R-Texas, has drafted a bill that would require, for all funding going to Pakistan, that the State Department certify that Pakistan was not providing sanctuary to bin Laden.
The State Department is already required by law to certify that the focus of the U.S. assistance to Pakistan is being met, and that no steps weaken democratic institutions or governance within the country.